Regulr polygons w/their diagonals drawn in can be viewd as graphs (w/ a vertex @Rachel Carter intersection), its helpfl to reformulate our initial questions in terms of graph theory rather than simple plane geometry. Here are the regular n-gons w/their diagonals for n = 3, 4, ..., 12.If we make every intersection pt a vertex, then these pics automatically become connectd, planar graphs. If we know the # of intersection points & the # of segments, we can then use Euler's formula to find the #…